Turbulence and Magnetic Field in High-β Plasma of Intracluster Medium

Transcription

1 Turbulence and Magnetic Field in High-β Plasma of Intracluster Medium Coma cluster of galaxies Dongsu Ryu UNIST (Ulsan National Institute of Science and Technology, Korea) KASI (Korea Astronomy and Space Science Institute, Korea) Hyesung Kang (PNU, Korea), T. W. Jones (Minnesota, USA), others 1/48

2 Magnetic field (and plasma) is everywhere! Earth s magnetic field reversal of magnetic field computer simulation strength ~ G (1 G = 10-4 T) interval ~ 0.1 to 50 million years the last event the Brunhes-Matuyama reversal of ~0.78 million years ago magnetosphere - shields harmful radiations from space history of reversal 2/48

3 Solar and Galactic magnetic field Sun s photosphere ~ 1 G sunspots ~ 1 kg interstellar medium ~ several μg molecular clouds ~ mg 3/48

4 The large-scale structure of the universe observation of galaxies clusters of galaxies filaments void regions the cosmic web simulation of matter distribution 4/48

5 100 h -1 Mpc Cosmic magnetic fields Mpc = 3.26 x 10 6 light-years h = Hubble constant / 100 km/s = ~0.7 void regions: B > ~10-16 G filaments of galaxies: B ~ 10 ng distribution of cosmological shocks clusters of galaxies: B ~ a few μg 5/48

6 Magnetic field is ubiquitous in the Universe. Star Magnetar ~ G Neutron star ~ G White dwarf ~ 10 6 G Ap/Bp star ~ 10 3 G Normal star ~ 1 G Molecular cloud ~ 10-3 G Interstellar medium ~ several x10-6 G Cluster of galaxies ~ a few x 10-6 G Filament of galaxies ~ G (?) Void ~ G (?) stronger field larger scale Early universe ~ G (?) Planck mass monopole ~ G 6/48

7 Clusters of galaxies MACSJ0717 aggregates of galaxies, which are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation MACSJ0717 Hubble space telescope image mostly star light The intracluster medium (ICM) optical (Hubble, white) X-ray (Chandra, blue) hot gas radio (VLA, red) cosmic rays the superheated plasma with T ~ a few to several kev, presented in clusters of galaxies 7/48

8 ICMs are dynamical: - large-scale flow motion - shocks - turbulence - magnetic fields - cosmic-rays Perseus cluster: X-ray Coma cluster: X-ray Radio relic in CIZA J /48

9 Some Evidence for turbulence in clusters - pressure fluctuations in Coma (Schuecker et al 2004) P/P ~ 0.1 n ~ 1/3 7/3 (P k ~ k -n ) -> consistent to Kolmogorov - X-ray surface brightness fluctuations in Coma (Churazov et al 2011) r/r ~ 0.1 n ~ 2 -> steeper than Kolmorogov (shock-dominated?) - line broadening limit in A1835 (Sanders et al 2010) v < 274 km/sec -> E turb / E tot <~ patchy Faraday rotation distributions in clusters (Murgia et al 2004) n ~ 0 for B -> broken power-law? - and etc 9/48

10 Turbulence in Coma cluster 250 kpc P ρ ~ k -5/3 (power spectrum of density) (XMM X-ray) Mach number of turbulence in ICMs, M turb, less than 1, ~ 0.5 if incompressible mode dominates 10/48

11 Magnetic fields in galaxy clusters appears in observations CIZA J Sausage relic Hydra North (van Weeren et al 2010) (Shea Brown) Faraday rotation measure (Vogt & Ensslin 2005) Coma cluster Relic halo 11/48

12 (Govoni & Feretti 2004) 12/48

13 Fluid quantities in the ICM size of clusters density of baryonic matter flow velocity gas temperature magnetic fields gas thermal energy gas kinetic energy cosmic-ray energy magnetic energy L size 2 n ~ 10 cm 3 υ ~ several 10 T 8 3 ~ 10 K c s ~ 10 km/s B µ E E E E 2 km/s 2 ~ a few G c A ~ 10 km/s thermal kinetic 20 ~ a few Mpc ~ 10 km flows are subsonic (M s ~ 0.5) and super-alfvenic (M A > 1) plasma beta is high β ~ 100 cosmic-ray magnetic β ~ 10 ~ erg/cm erg/cm 3 ~ a few 10 ~ a few 10 P P gas magnetic erg/cm erg/cm 13/48 3 3

14 A model for turbulence and magnetic fields in clusters of galaxies large-scale structure formation (Ryu et al 2008) gravitational collapse, mergers, & flow motions shocks in the LSS of the Univ shock dissipation generation of vorticity stretching and compression development into turbulence seed fields small-scale or turbulent dynamo amplification of magnetic fields 14/48

15 Origin of turbulence and magnetic fields in clusters - generation of turbulence structure formation? AGN outflows? wakes of galaxies? instabilities? etc - generation of seed fields primordial? or astrophysical? - amplification of seed fields by turbulent flow motions 15/48

16 Observation of shocks in clusters: X-ray The Bullet Cluster M X 3.0 (no associated radio relic) (Markevitch 2006) M X 2.5 (Shimwell et al. 2015) Cluster A665 shock cold front cold front M X = 3± 0.6 (no associated radio relic) (Dasadia et al. 2016) 16/48

17 Observation of shocks in clusters: radio relics Giant Gischt Relic Sausage relic Abell PLCKG (van Weeren et al. + Ryu 2016) 17/48

18 Shock waves induced during the formation of the large-scale structure of the universe Shock waves in a simulated clusters of galaxies strong accretion shocks with M>10 (green) weak inreacluster shocks with M<4 (orange) Simulation credits: Vazza, Jones, Gheller, Bruggen, Brunetti & Ryu, on ITASCA at Minnesota Supercomputing Institute (MSI). Visualization credits: 3D renderings (Jones) with Hierarchical Volume Rendering, 'HVR, developed in the LCSE at the University of Minnesota. Critical support from MSI (D. Porter) and LCSE (M. Knox). 18/48

19 Shocks around a simulated cluster in a 2D slice (in the plane through the center) (6h -1 Mpc) 2 (Hong, Ryu, Kang, & Cen 2014) gas density temperature shock Mach no. R200 accretion shock from voids to clusters Structures of shocks in galaxy clusters are complex! shocks due to mergers of sub-clusters 20 infall shock (accretion from WHIM to hot IGM) 20/48

20 Vorticity generated at cosmological shocks - directly at interacting and curved shocks interacting shocks div(v) - by the baroclinic term 1 ϖ bc = 2 ρ ρ p ω ϖ ρ 1 ρ 2 U n R cs ~ at shocks 2 1 ( ρ2 ρ1) ρ ρ U n R preshock density postshock density preshock flow speed unit normal to shock surf. curvature radius of surf. baroclinity constant ρ constant p due to entropy variation induced at shocks Magnitude of vorticity or enstropy (e) enhanced by stretching and compression increases during the development of turbulence (Porter, Jones, Ryu 2015) 21/48 2

21 X-ray Vorticity in a cluster complex shocks (Ryu, Kang, Cho, & Das 2008) velocity field ω x ω (25 h -1 Mpc) 2 2D slice 22/48

22 Theory of turbulence Kolmogorov's theory for incompressible hydrodynamic turbulence: it is based on the notion that that large eddies can feed energy to the smaller eddies and these in turn feed still smaller eddies, resulting in a cascade of energy from the largest eddies to the smallest ones. a schematic representation of the turbulent energy cascade from large to small scales on dimensional grounds, the only way of writing ε (energy transfer rate) in terms of V (velocity) and l (scale) is ε ~ V 2 ~ t V P k ~ l ~ V 1/3 k 5/3 power spectrum of velocity! l 3 ~ constant the spectrum of Kolmogorov turbulence 23/48

23 Turbulence in high resolution simulations of galaxy clusters vorticity in the plane through the cluster center (Miniati 2013) 24/48

24 Solenoidal & compressional components of turbulence fraction of turbulent kinetic energy flux in compressive component mostly in solenoidal (incompressible) component the fraction of compressional component <~ 10 % (Vazza et al + Ryu 2016) distance from cluster center 25/48

25 Turbulence energy of in the ICM assuming that turbulence is contained in vortical motions M turb ~ 1 (transonic turbulence) in filaments clusters M turb < ~1 (subsonic turbulence) E turb /E therm ~ inside and outskirts of clusters (Ryu et al 2008) 26/48

26 Origin of turbulence and magnetic fields in clusters - generation of turbulence structure formation? AGN outflows? wakes of galaxies? instabilities? etc - generation of seed fields primordial? or astrophysical? - amplification of seed fields by turbulent flow motions 27/48

27 Seed magnetic fields in the large-scale structure (LSS) of the universe Suggestions include: - generation in the early universe (e.g., see Widrow, Ryu et al 2012 for review) e.g.) during the electroweak phase transition (t~10-12 sec) during the quark-hadron transition (t~10-5 sec) uncertain but maybe challenging (?) - generation before the formation of the LSS of the universe through plasma physical processes (e.g., see Ryu et al 2012 for review) e.g.) Biermann battery or Weibel Instability at shocks (Kulsrud, Cen, Ostriker, & Ryu 1997) (Medvedev & Loeb 1999) instabilities, thermal fluctuations, photo-ionization and etc weak (~ G) and some at small scales, yet most promising(?) - astrophysical processes e.g.) magnetic fields from the first stars maybe not the first magnetic field Origin of seeds for comic magnetic fields is uncertain! 28/48

28 Laboratory reproduction of magnetic field generation through the Biermann battery mechanism at shock waves (Kulsrud, Cen, Ostriker, Ryu 1997) theory: predicted the generation of seeds of cosmic magnetic fields at curved intergalactic shock waves ~ G by t ~ 10 9 years or t~ 1/10 t univ-age experiment: after scaling, confirmed the generation of G magnetic field in the cosmic scale (Gregori et al 2012) 29/48

29 Toward magnetic field generation by the Weibel instability at collisionless shocks theory: requires magnetic fields at astrophysical collisionless shocks what if a shock forms in collisionless plasma with no or weak magnetic field? (Huntington et al 2015) simulation: predicts magnetic field generation by the Weibel instability experiments: confirms the prediction 30/48

30 Origin of turbulence and magnetic fields in clusters - generation of turbulence structure formation? AGN outflows? wakes of galaxies? instabilities? etc - generation of seed fields primordial? or astrophysical? - amplification of seed fields by turbulent flow motions 31/48

31 Turbulence with magnetic fields Magnetic fields play an important or crucial role with magnetic field fluid drags magnetic field magnetic field exerts tension and pressure fluid and magnetic field moves together ( frozen ) with large magnetic Reynolds number υ + t B t ( ) 1 1 ( ) υ υ + p = B B = ρ ( ) B υ 4πρ B o Turbulence + magnetic field Magnetohydrodynamic turbulence 32/48

32 Turbulence in astrophysical environments - Turbulence in the interstellar medium (ISM) with β ~ 1 (strong regular or background field field) Goldreich & Sridhar model - Turbulence in the intracluster medium (ICM) with β >> 1 (no regular or background field field) super-alfvenic turbulence magnetic fields are amplified by turbulence from weak seed fields turbulence dynamo or small-scale dynamo - Two turbulences should have different properties! 33/48

33 Small-scale dynamo of MHD turbulence with weak initial field (Jo, Ryu, et al, in preparation) growth of magnetic energy E kin at saturation E mag /E kin ~ 2/3 exponential growth linear growth E mag saturation 34/48

34 Evolution of magnetic field power spectrum at early stages (From Cho) 1 inverse cascade linear growth exponential growth 35/48

35 Power spectrum at saturation E kin E mag 37/48

36 A model for magnetic fields in galaxy clusters - vorticity generated at shocks and also due to baroclinity - turbulence developed - standard picture of MHD turbulence applied - magnetic field produced by turbulence dynamo In galaxy clusters - B ~ a few μg - L int ~ a few x 10 kpc ω B (Ryu et al 2008) 38/48

37 Magnetic fields in clusters (Cho & Ryu 2009) energy injection scale: turbulent flow speed: L inj ~ a few x 100 kpc v turb ~ several x 10 2 km/s eddy turn-over time: t eddy ~ several x 10 8 yrs - magnetic fields in clusters <B> ~ a few μg, L int ~ several x 10 kpc the integral scale is a length scale of magnetic field, which would be relevant to Faraday rotation measure L int = 2π ( E / k) dk / B E B dk 39/48

38 Large-scale magnetic fields? CIZA J (sausage radio relic) (van Weeren et al 2010) magnetic field geometry: large-scale field of ~ 2 Mpc? 40/48

39 Laboratory reproduction of magnetic field amplification through turbulence (turbulence or small-scale dynamo): TDYNO (Tzeferacos et al + Ryu 2016) ~ 4.5x10 8 light-years several x100 kg In lab experimental exploration for the turbulence dynamo origin of magnetic fields in clusters of galaxies ~ a few µg In clusters 41/48

40 Plasma properties in of high β plasma in the ICM size of clusters Coulomb mean free path gyro-radius of thermal protons gyro-radius of thermal electrons ion inertial length electron skin depth Debye length plasma parameter Λ 4π n λ e 3 Debye = 4π k e 4π 2 3/ 2 n l 1 / 2 e ~ a few kpc ~ L /10 Coul 6 r gp ~ 10 km r ge λ i λ e λ D 3 ~ 10 km 4 ~ 10 km 2 ~ 10 km ~ 10 km 17 Λ ~ 10 T 3 / 2 e 20 ~ a few Mpc ~ 10 km ~ thermal K.E. Coulomb P.E. plasma is collisionless (l Coul >> r gp ) and weakly coupled (Λ >>1) 42/48 L size size 3/2 3

41 Intracluster media (ICMs) of galaxy clusters - may be treated as fluids on the cluster scale, L size > ~ Mpc - host turbulence, which would be hydrodynamic (HD) on largest scales but MHD on smaller scales - contain shock waves with M s ~ a few - below Coulomb collision scale l Coul ~ a few kpc, plasma effects may enter - gyro and inertial scales of thermal particles are much smaller than l Coul - with Λ >> 1, they are good plasmas, e.g., carry plasma waves We need to study fluid phenomena as well plasma phenomena to understand ICMs! 43/48

42 Viscosity and resistivity the ICM kinetic viscosity p p p p p p p p t l l 2 therm ~ ~ υ ν resistivity p e p t c 2 ) / ( ~ ω η = 2 1/ 2 4 e e p m e n π ω high magnetic Prandtle number? or larger? ~ η ν = P m or substantially smaller? much smaller than viscosity? 44/48

43 Turbulence with B 0 << δb and large P m - Time evolution of kinetic and magnetic energies P m >>1 E kin at saturation magnetic energy >> kinetic energy P m =1 E mag 45/48

44 - Power spectrum at saturation with ν >> η, V k << B k E mag E M ~ constant, E ~ in the inertial range K k 3 E kin P m >>1 P m =1 46/48

45 Summary - Magnetic field is ubiquitous, even in the large-scale structure of the universe. - Magnetic field of ~ a few μg of coherence length of ~ several 10 kpc in clusters of galaxies could be explained by turbulence (small-scale) dynamo. - But there are a number of issues to be further resolved e.g., mean-free-path ~ a few kpc (size of clusters ~ a few Mpc) plasma effects in collisionless regime? Mpc-scale magnetic field? 47/48

46 Thank you! 48/48